﻿<p>The vertical circular arc segment is defined as an arc using the inherited attributes from <i>IfcAlignment2DVerticalSegment</i> and the following additional curve parameters <i>Radius</i> as the radius of the circular arc, and <i>IsConvex</i> to indicate the whether the circular arc defines a sag (i.e. concave, increasing gradiant) or a crest (i.e. convex, decreasing gradiant).</p>

<p>The circular arc is described by:</p>
<ul style="list-style-type: none">
 <li>x = offset as length measure relative to start of curve segment (i.e. 0 is at head).</li>
 <li>g<sub>1</sub> = <i>StartGradient</i> as ratio measure<li>
 <li>R = <i>Radius</i> as length measure</li>
</ul>

<p>For crest curves (where <i>IsConvex</i> is True), the elevation of a point along the curve (relative to <i>StartHeight</i>) is defined as:</p>
<img src="../../../figures/ifcalignment2dversegcirculararc-formula-concave.png"/>
<table>
<tr><td><img src="../../../figures/ifcalignment2dversegcirculararc-convex.png" /></td><td style="vertical-align: bottom">start point provided by <i>StartDistAlong</I> and <i>StartHeight</i><br>instanteneous gradient provided by <i>StartGradient</i>, <br>and length provided by <i>HorizontalLength</i></td></tr>
<tr><td><p class="figure">Figure 3 &mdash; Alignment vertical arc segment convex</p></td><td>&nbsp;</td></tr>
</table>
<p>&nbsp;</p>

<p>For sag curves (where <i>IsConvex</i> is False), the elevation of a point along the curve (relative to <i>StartHeight</i>) is defined as:</p>
<img src="../../../figures/ifcalignment2dversegcirculararc-formula-convex.png"/>
<table>
<tr><td><img src="../../../figures/ifcalignment2dversegcirculararc-concave.png" /></td><td style="vertical-align: bottom">start point provided by <i>StartDistAlong</I> and <i>StartHeight</i><br>instanteneous gradient provided by <i>StartGradient</i>, <br>and length provided by <i>HorizontalLength</i></td></tr></tr>
<tr><td><p class="figure">Figure 4 &mdash; Alignment vertical arc segment concave</p></td><td>&nbsp;</td></tr>
</table>
